An invitation to quantum tomography

Summary.  We describe quantum tomography as an inverse statistical problem in which the quantum state of a light beam is the unknown parameter and the data are given by results of measurements performed on identical quantum systems. The state can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We present consistency results for pattern function projection estimators and for sieve maximum likelihood estimators for both the density matrix of the quantum state and its Wigner function. We illustrate the performance of the estimators on simulated data. An EM algorithm is proposed for practical implementation. There remain many open problems, e.g. rates of convergence, adaptation and studying other estimators; a main purpose of the paper is to bring these to the attention of the statistical community.     

Structural learning with time-varying components: tracking the cross-section of financial time series

Summary.  When modelling multivariate financial data, the problem of structural learning is compounded by the fact that the covariance structure changes with time. Previous work has focused on modelling those changes by using multivariate stochastic volatility models. We present an alternative to these models that focuses instead on the latent graphical structure that is related to the precision matrix. We develop a graphical model for sequences of Gaussian random vectors when changes in the underlying graph occur at random times, and a new block of data is created with the addition or deletion of an edge. We show how a Bayesian hierarchical model incorporates both the uncertainty about that graph and the time variation thereof.     

THE POTENTIAL OF INTEGRATED POPULATION MODELLING†

Recent work has shown how the Kalman filter can be used to provide a simple framework for the integrated analysis of wild animal census and mark‐recapture‐recovery data. The approach has been applied to data on a range of bird species, on Soay sheep and on grey seals. This paper reviews the basic ideas, and then indicates the potential of the method through a series of new applications to data on the northern lapwing, a species of conservation interest that has been in decline in Britain for the past 20 years. The paper analyses a national index, as well as data from individual sites; it looks for a change‐point in productivity, corresponding to the start of the decline in numbers, considers how to select appropriate covariates, and compares productivity between different habitats. The new procedures can be applied singly or in combination.     

矩阵A的中心化子可表成A的方阵多项式的充要条件

n阶矩阵A的中心化子C(A) ={B∈Pn×n|AB =BA} ,P[A] ={f(A)∈Pn×n|f(x)∈P[x] } 本文给出了C(A) =P[A] ,即A的中心化子可表成A的矩阵多项式的充要条件     

实对称矩阵的广义Cholesky分解及扰动

设N为实对称矩阵，证得当p（N）〈1时。存在唯一分解J＋N=（I＋L）J（I＋L）^T；在此基础上，得到一些新的扰动结论，对以往的结果略有改进。     

正定矩阵的Hadamard不等式

本文利用文［２］的结果给出了正定矩阵的Ｈａｄａｍａｒｄ不等式，进而给出了两类正定矩阵Ｈａｄａｍａｒｄ积的Ｈａｄａｍａｒｄ不等式．     

资金利税率取代经济效益综合指数的实证研究

在介绍国家统计局推行的经济效益综合指数之后,利用河南省17个市、地独立核算工业企业的资料,通过实证研究和指标分解,提出了用资金利税率指标代替经济效益综合指数的建议。     

信号相关性与DOA估计

窄带波达方向(DOA)估计模型中,相干信号的问题很容易引起混淆。一些文献简单地认为频率不同的信号是不相干的,而频率相同的信号就是相干信号。因此,在建立不相干信号的DOA估计模型时,采用不同中心频率的信号,而使用的方向矩阵却采用同一个信号频率,该文提出,当信号中心频率不同时,应采用各自相应的频率来建立方向矩阵。其DOA估计应采用宽带信号的DOA估计方法,也就是应该对不同的频率进行聚焦。而采用同一个频率来建立的方向矩阵恰好同聚焦后的信号模型相同,因此,其估计结果也就是正确的。但这样的信号模型与事实并不相符。该文严格按照相干信号的定义证明了只有频率和初始相位都相同的窄带信号才是相干信号,最后通过计算机仿真验证了这一点。     

矩阵奇异值的估计

本文研究矩阵奇异值估计的相关问题,给出了一些矩阵奇异值极值的结论。     

多元线性模型共同均值矩阵参数的线性估计的可容许性特征

讨论了一般多元线性模型共同均值矩阵参数的线性组合函数SXO的线性估计在一切估计类中的A－可容许性问题，并得到了它的充要条件。